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Graph theory has successfully used to solve a wide range of problems encountered in diverse fields such as medical sciences, neural networks, control theory, transportation, clustering analysis, expert systems, image capturing, and network…
Identification theory for causal effects in causal models associated with hidden variable directed acyclic graphs (DAGs) is well studied. However, the corresponding algorithms are underused due to the complexity of estimating the…
In Functional Data Analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional…
Multivariate functional data arise in a wide range of applications. One fundamental task is to understand the causal relationships among these functional objects of interest, which has not yet been fully explored. In this article, we…
In the past decade, with the development of big data technology, an increasing amount of patient information has been stored as electronic health records (EHRs). Leveraging these data, various doctor recommendation systems have been…
We investigate the automatic differentiation of hybrid models, viz. models that may contain delays, logical tests and discontinuities or loops. We consider differentiation with respect to parameters, initial conditions or the time. We…
Learning from longitudinal electronic health records is limited if it does not capture the temporal trajectories of the patient's state in a clinical setting. Graph models allow us to capture the hidden dependencies of the multivariate…
Motivated by the need to study the molecular mechanism underlying Type 1 Diabetes (T1D) with the gene expression data collected from both the patients and healthy controls at multiple time points, we propose an innovative method for jointly…
The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…
In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…
Longitudinal analysis is important in many disciplines, such as the study of behavioral transitions in social science. Only very recently, feature selection has drawn adequate attention in the context of longitudinal modeling. Standard…
Understanding the functional architecture of the brain in terms of networks is becoming increasingly common. In most fMRI applications functional networks are assumed to be stationary, resulting in a single network estimated for the entire…
Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a…
Understanding associations between paired high-dimensional longitudinal datasets is a fundamental yet challenging problem that arises across scientific domains, including longitudinal multi-omic studies. The difficulty stems from the…
The data drawn from biological, economic, and social systems are often confounded due to the presence of unmeasured variables. Prior work in causal discovery has focused on discrete search procedures for selecting acyclic directed mixed…
Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs…
Epileptic seizures are neurological disorders characterized by abnormal and excessive electrical activity in the brain, resulting in recurrent seizure events. Electroencephalogram (EEG) signals are widely used for seizure diagnosis due to…
Emotion Recognition from EEG signals has long been researched as it can assist numerous medical and rehabilitative applications. However, their complex and noisy structure has proven to be a serious barrier for traditional modeling methods.…
Autism Spectrum Disorder (ASD) is a neurodevelopmental condition characterized by varied social cognitive challenges and repetitive behavioral patterns. Identifying reliable brain imaging-based biomarkers for ASD has been a persistent…
There are many functions which are continuous everywhere but non-differentiable at some or all points such functions are termed as unreachable functions. Graphs representing such unreachable functions are called unreachable graphs. For…